Best Known (53−16, 53, s)-Nets in Base 49
(53−16, 53, 14710)-Net over F49 — Constructive and digital
Digital (37, 53, 14710)-net over F49, using
- net defined by OOA [i] based on linear OOA(4953, 14710, F49, 16, 16) (dual of [(14710, 16), 235307, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4953, 117680, F49, 16) (dual of [117680, 117627, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(7) [i] based on
- linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(497, 31, F49, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,49)), using
- discarding factors / shortening the dual code based on linear OA(497, 49, F49, 7) (dual of [49, 42, 8]-code or 49-arc in PG(6,49)), using
- Reed–Solomon code RS(42,49) [i]
- discarding factors / shortening the dual code based on linear OA(497, 49, F49, 7) (dual of [49, 42, 8]-code or 49-arc in PG(6,49)), using
- construction X applied to Ce(15) ⊂ Ce(7) [i] based on
- OA 8-folding and stacking [i] based on linear OA(4953, 117680, F49, 16) (dual of [117680, 117627, 17]-code), using
(53−16, 53, 125481)-Net over F49 — Digital
Digital (37, 53, 125481)-net over F49, using
(53−16, 53, large)-Net in Base 49 — Upper bound on s
There is no (37, 53, large)-net in base 49, because
- 14 times m-reduction [i] would yield (37, 39, large)-net in base 49, but